José Simental

collaborators

3 papers

math.RT2025

The elliptic Hall algebra and the double Dyck path algebra

Nicolle Gonzalez, Eugene Gorsky, Jose Simental

We show that the positive half $E_{q, t}^{>}$ of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q…

math.RT2023

Cluster algebras in Lie and Knot theory

Mikhail Gorsky, José Simental

This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.

math.CO2023

Higher rank $(q, t)$ -Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem

Nicolle González, José Simental, Monica Vazirani

We introduce the higher rank $(q, t)$ -Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a…

The elliptic Hall algebra and the double Dyck path algebra

Cluster algebras in Lie and Knot theory

Higher rank (q,t)-Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem

Higher rank $(q, t)$ -Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem